If seizing and governing a city is necessary to help the citizens and prevent ISIS or other terrorist groups from gaining control and influence then I think the U.S. is obligated to do so. While this isn't always in our best interests and could cost many lives, if the long-term result is peace and protection of human rights then it needs to be done.
While I do believe that the United States should be involved in the governing of foreign cities and countries, I think that that power should be limited and only exercised in situations of crisis for a limited amount of time. Instead of simply controlling another country, systems should be put in place so that once an effective government is established, agreements and coalitions between governments can be created to ensure the proper governance of these cities or countries.
It would be more desirable if the United Nations or even NATO could step in and provide neutral peacekeeping and governance as an interim measure during times of conflict. It is not appropriate for foreign sovereign nations to occupy and take over governance as there are simply too many vested interests to ensure the interests of the local people are upheld properly.
The United States should entrust its allies to governing Raqqa and other Middle Eastern areas. Allies that are more in tune with the Islamic culture and are able to react appropriately to fundamentalist movements and appease discontented factions do a better job and keep this country out of the affairs of other countries. This enables the U.S. to continue to exert influence in the region without having to maintain bases and troops, or be the target of radical factions. Exiting the region would also be seen as a favorable move by many groups who otherwise hold the U.S. responsible for the source of their unhappiness.